Tax multiplier

Topic: Government Budget, Fiscal Policy and FRBM · NCERT: Class 12, Ch 5 "Government Budget and the Economy"

Meaning

The tax multiplier is the change in equilibrium income (ΔY) caused by a one-rupee change in lump-sum taxes (a fixed tax amount that does not change with income): ΔY/ΔT = −c/(1 − c), where c is the marginal propensity to consume (MPC), the share of each extra rupee of income that people spend.

It is negative, because a higher tax lowers income. Its size is always exactly 1 less than the government expenditure multiplier. This is why a rupee of government spending lifts output more than a rupee of tax cut.

Explanation

How it works: taxes act only through consumption

• Government purchases (G) are part of aggregate demand (AD), the total planned spending in the economy. So G raises AD directly, rupee for rupee.
• Taxes (T) work indirectly, through disposable income (YD), the money households have left to spend or save:
• YD = Y − T + TR (TR = transfers such as pensions and scholarships)
• A tax change first changes YD.

• Households change their spending by only c times that amount. They save the rest.

• The model (NCERT Class 12, Box 5.1):

• Consumption: C = C̄ + c(Y − T + TR), where C̄ is autonomous consumption (spending that happens even at zero income).
• Equilibrium: Y* = (C̄ − cT + cTR + I + G) / (1 − c)

• G carries 1/(1 − c). T carries −c/(1 − c). The extra c on T is the whole story.

• Effect on the AD curve: a higher lump-sum tax lowers consumption by the same amount at every income level.

• So AD shifts down in parallel.
• Its slope does not change.

Why it is negative and smaller in size

• Negative sign:

• tax rises → disposable income falls → consumption falls → income falls.

• Smaller size:

• A ₹100 tax cut does not reach AD as ₹100.
• Households save (1 − c) of it. So the first round of spending is only cΔT.
• The spending multiplier counts a full first round of ₹100. The tax multiplier misses that round.
• So |tax multiplier| = G multiplier − 1.

MPC (c)	G multiplier 1/(1 − c)	Tax multiplier −c/(1 − c)
0.8	5	−4
0.75	4	−3

Worked example (c = 0.8, NCERT Example 5.1)

• Tax cut of ₹100, round by round:
• Round 1: ₹80 is spent (₹20 saved).
• Round 2: ₹64. Round 3: ₹51.2. And so on.

• Total: 100 × (0.8 + 0.8² + …) = 100 × 0.8/0.2 = ₹400.

• G rise of ₹100: 100 × (1 + 0.8 + 0.8² + …) = ₹500.

• The gap is only the first round (₹100).
• Exercise 5 check: C = 100 + 0.75Y, I = 200, G = 150, net taxes = 100.
• Y = 100 + 0.75(Y − 100) + 200 + 150, so Y = 1,500.
• Tax multiplier = −0.75/0.25 = −3. So a ₹100 rise in taxes would cut Y by ₹300.

What makes it bigger or smaller

• Higher MPC (c): a larger share of each rupee of tax change is spent, so the multiplier is bigger. With c = 0.8 it is −4. With c = 0.75 it is −3.
• Proportional taxes (T = tY, a flat share of income):
• Each round of spending loses some income to tax.
• The effective MPC falls to c(1 − t), so every multiplier becomes smaller.

• Example (Exercise 9, c = 0.75, t = 0.2): the transfer multiplier falls from 3 to 0.75/0.4 = 1.875.

• Real-world leakages: saving, imports and rising interest rates all drain demand. So actual multipliers are much smaller than the textbook 4 or 5 [4].

In India

• Where it is used: the Union Budget, presented as the Annual Financial Statement (Art. 112), sets tax rates each year. Any change in income tax or other taxes works on output through this multiplier.
• The law that limits it: since 2003 the FRBM Act caps the deficit. So a tax cut that widens the deficit must be weighed against spending options that do more for growth.
• Indian evidence on tax cuts and transfers:
• NIPFP (Bose and Bhanumurthy, 2015): revenue spending and transfers have a multiplier of only about 0.99. Capital expenditure has about 2.45.
• RBI Working Paper 07/2013: capital outlay has an impact multiplier of 1.29 (peak 3.56). Revenue expenditure has only 0.37 [2].

• RBI Bulletin (June 2021): the capital expenditure multiplier in India is "known to be higher than 2" [3].

• What this means: a tax cut or cash transfer puts money in households' hands, so it works like revenue spending. Part of it is saved or spent on imports. Capex usually gives more output per rupee of deficit.

Don't confuse with

• Government expenditure multiplier: 1/(1 − c), which is positive. It is always 1 more than the tax multiplier in size, because G enters AD directly.
• Transfer multiplier: c/(1 − c). It is the same size as the tax multiplier but positive, because a transfer is a "negative tax".
• Balanced budget multiplier: equal rises in G and T give 1/(1 − c) − c/(1 − c) = 1, not zero. The tax multiplier alone is always negative.
• Multiplier with proportional tax: 1/[1 − c(1 − t)]. This tax changes the slope of AD (AD becomes flatter). A lump-sum tax only shifts AD down in parallel.

Prelims Hooks

• Tax multiplier = −c/(1 − c). With c = 0.8 it is −4. With c = 0.75 it is −3.
• Its absolute value is always exactly 1 less than the G multiplier (5 vs 4, 4 vs 3).
• Trap: "A tax cut of ₹100 raises income as much as ₹100 of government spending." False. With c = 0.8, the tax cut gives ₹400 and the spending gives ₹500.
• Transfer multiplier = tax multiplier with the sign flipped: c/(1 − c).
• Balanced budget multiplier = 1 for any MPC, with lump-sum taxes. It comes from subtracting the tax multiplier from the G multiplier.
• A lump-sum tax shifts AD down in parallel. It does not change the slope.

Mains Points

• Tax cut or spending? The choice matters for growth.
• Rupee for rupee, the tax multiplier is smaller than the spending multiplier. Households save part of any tax relief.
• Indian evidence says capex does the most: capital outlay has an impact multiplier of 1.29, against 0.37 for revenue spending [2].

• So when FRBM limits leave little room to borrow, raising capex usually does more for growth than cutting taxes by the same amount.

• Balanced budget route to growth.

• The tax multiplier is 1 less than the G multiplier. So spending ₹100 more and paying for it with ₹100 more tax still raises output by ₹100.

• A country with high public debt, like India, can use this to support demand without breaking FRBM deficit targets.

• Tax design and stability.

• A proportional income tax gives a smaller multiplier, but it works as an automatic stabiliser (it acts on its own, without a new government decision).
• Tax collections rise in a boom and fall in a slump, which cushions disposable income. The IMF notes such stabilisers "tend to be larger in advanced economies" [4].
• In India this effect is weaker, so deliberate counter-cyclical action, like the 2020-21 COVID response, matters more.

Related concepts

• Fiscal policy
• Lump-sum tax
• Government expenditure multiplier
• Transfer multiplier
• Balanced budget multiplier
• Fiscal multiplier

Read more

• Fiscal policy and the multipliers